Journal of Fluid Mechanics

A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence

P. A.  Durbin a1
a1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW

Article author query
durbin pa   [Google Scholar] 


A new definition of concentration fluctuations in turbulent flows is proposed. The definition implicitly incorporates smearing effects of molecular diffusion and instrumental averaging. A stochastic model of two-particle dispersion, consistent with this definition, is formulated. The stochastic model is an extension of Taylor's (1921) model and is consistent with Richardson's $\frac{4}{3}$ law. Its predictions of concentration fluctuations are contrasted with predictions based on a more usual one-particle model.

The present model is used to predict fluctuations in three case studies. For example (case (i) of § 6), downstream of a linear concentration gradient we find $\overline{c^{\prime 2}}=\frac{1}{2}m^2(\overline{Z^2}-\overline{\Delta^2})$. Here m is the linear gradient, $\overline{Z^2}$ is related to centre-of-mass dispersion and $\overline{\Delta^2}$ is related to relative dispersion (see equation (3.1)). The term $\frac{1}{2}m^2\overline{Z^2} $ represents net production of fluctuations by random centre-of-mass dispersion, whereas $\frac{1}{2}m^2\overline{\Delta^2} $ represents net destruction of fluctuations by relative dispersion. Only the first term is included in the usual one-particle model (Corrsin 1952).

(Published Online April 19 2006)
(Received October 15 1979)
(Revised January 25 1980)